I need help creating a mathematical proof for a game strategy. Here's a description of the game:

1. Start with an integer, n, greater than or equal to 2

2. Make a list whose sum is equal to n

3. Multiply the numbers in your list to obtain a score

4. The highest score wins

The best strategy (i believe) is to have as many 3's in your list as possible and include only one 2 or 4 if needed.

For example, the best list for an n of 20

is 3,3,3,3,3,3,2

n of 14: 3,3,3,3,2

n of 10: 3,3,4